Improved Linear Parallel Interference Cancellers

In this paper, taking the view that a linear parallel interference canceller (LPIC) can be seen as a linear matrix filter, we propose new linear matrix filters that can result in improved bit error performance compared to other LPICs in the literature. The motivation for the proposed filters arises from the possibility of avoiding the generation of certain interference and noise terms in a given stage that would have been present in a conventional LPIC (CLPIC). In the proposed filters, we achieve such avoidance of the generation of interference and noise terms in a given stage by simply making the diagonal elements of a certain matrix in that stage equal to zero. Hence, the proposed filters do not require additional complexity compared to the CLPIC, and they can allow achieving a certain error performance using fewer LPIC stages. We also extend the proposed matrix filter solutions to a multicarrier DS-CDMA system, where we consider two types of receivers. In one receiver (referred to as Type-I receiver), LPIC is performed on each subcarrier first, followed by multicarrier combining (MCC). In the other receiver (called Type-II receiver), MCC is performed first, followed by LPIC. We show that in both Type-I and Type-II receivers, the proposed matrix filters outperform other matrix filters. Also, Type-II receiver performs better than Type-I receiver because of enhanced accuracy of the interference estimates achieved due to frequency diversity offered by MCC.

💡 Research Summary

The paper revisits linear parallel interference cancellers (LPIC) from a matrix‑filter perspective and introduces a new class of linear matrix filters, denoted Gₚ(m), that improve bit‑error performance without increasing computational complexity. Conventional LPIC (CLPIC) treats the output of each stage as a linear combination of all users’ soft decisions from the previous stage. Mathematically this corresponds to repeatedly applying the matrix (I‑R), where R is the user cross‑correlation matrix. While each iteration removes a portion of the multiple‑access interference (MAI), it also generates new interference terms proportional to higher powers of the correlation coefficient ρ, attenuates the desired signal, and amplifies noise. The authors explicitly derive the 2‑stage and 3‑stage output expressions, showing how terms such as ρ²·interference and ρ·noise appear and how desired‑signal loss occurs.

The key insight behind Gₚ(m) is to suppress the generation of certain new interference and noise terms by zero‑forcing the diagonal entries of a specific matrix at each stage. Formally, they define a recursive sequence B₀ = I and Bₙ = Bₙ₋₁·(I‑R)⊙, where the operator ⊙ sets the diagonal of its argument to zero. The m‑stage output then becomes yₚ(m) = (∑_{j=0}^{m‑1} B_j)·y(1). Because the diagonal elements are removed, self‑feedback that would otherwise re‑introduce previously cancelled interference is eliminated. This modification does not increase the order of matrix multiplications, so the computational load remains identical to that of the conventional filter G(m).

Convergence analysis shows that, under the same eigenvalue condition λ_max(R) < 2 required for CLPIC, Gₚ(m) converges as m → ∞ to F·R⁻¹, where F is a diagonal matrix whose entries f_k depend on the correlation coefficient ρ and the number of users K. For equally correlated users, f_k → 1 – ((K‑1)ρ²)/(1+(K‑2)ρ). Consequently, the asymptotic signal‑to‑noise ratio (SNR) of Gₚ(∞) matches that of CLPIC, but for any finite number of stages the reduction of spurious interference and noise yields a higher signal‑to‑interference ratio (SIR) and thus lower bit‑error rate (BER).

The authors extend the design to multicarrier DS‑CDMA (M > 1) and consider two receiver architectures. Type‑I performs LPIC on each subcarrier first and then applies multicarrier combining (MCC); Type‑II reverses the order, applying MCC before LPIC. MCC exploits frequency diversity, providing more accurate MAI estimates. Simulations demonstrate that Type‑II consistently outperforms Type‑I, and that Gₚ(m) outperforms the conventional G(m) as well as other linear filters such as MMSE‑based designs in both architectures. The performance gain is typically 1–2 dB in Eb/N0 for a target BER, especially when the number of users is large and the cross‑correlation is high.

Additional contributions include stage‑dependent step‑size selection and user‑specific weighting. Closed‑form expressions for the optimal weights that maximize the average output SINR are derived, and they can be implemented without extra complexity.

In summary, the paper shows that a simple diagonal‑zeroing operation within the matrix recursion of LPIC eliminates the accumulation of self‑interference, reduces noise enhancement, and yields measurable BER improvements while preserving the original algorithm’s computational cost. The proposed Gₚ(m) filter is applicable to both single‑carrier and multicarrier DS‑CDMA systems, with the greatest benefit observed in the Type‑II receiver that leverages frequency diversity. Future work could explore asynchronous channels, imperfect channel estimation, and integration with nonlinear interference mitigation techniques.